Qualitative Studies with Microwaves

Transcription

1 Qualitative Studies with Microwaves Physics 401, Spring 2015 Eugene V. Colla

2 The main goals of the Lab: Refreshing the memory about the electromagnetic waves propagation Microwaves. Generating and detecting of the microwaves Microwaves optic experiments This is two weeks Lab 2

3 The microwave range includes ultra-high frequency (UHF) (0.3 3 GHz), super high frequency (SHF) (3 30 GHz), and extremely high frequency (EHF) ( GHz) signals. Microwave Electromagnetic *by spectrum* courtesy Wikipedia 3

4 Microwave oven (2.45GHz) Communication ( GHz) Satellite TV (4-18GHz) Radar (up to 110GHz) Motion detector (10.4GHz) Weather radar (8-12Ghz) *by courtesy Wikipedia 4

5 D E B t (1) (3) B 0 (2) D H J t D (1) and (4) can be rewritten as If = 0 and J = 0 and taking in account that B H (4) E James Clerk Maxwell ( ) E x E E x y z y z D 0 H D t 5

6 Y Now assuming that plane wave propagate in z direction and what leads to E y =E z =0 and H x =H z =0 Now (3) and (4) could be simplified as X E x H y z where o r E x H y z t H z y E t o r y (5) (6) 0 is the free space permeability, 0 is the free space permittivity r is permeability of a specific medium, r is permittivity of a specific medium 6

7 Y Combining (5) and (6) (see Lab write-up for more details) we finally can get the equations of propagation of the plane wave: X H y E x E 1 E z v t 2 2 x x z H H 2 2 y 1 y (7) (8) z v t where E cos( ) x Ex0 t kx H cos( - ) y H y0 t kx Solution for (7) and (8) can found as Hy where Z known as characteristic impedance of medium 2 k is wave vector and is defined as k or k v For free space ( r =1 and r =1) Z fs 0 0 v 1 E ZH Ex or x y 377ohms 7

8 X E cos( ) x Ex0 t kx H cos( - ) y H y0 t kx E x H y z Y v 1 H y E x Z E x ZH y k 2 or k v Z fs ohms For free space ( r =1 and r =1) 8

9 Vacuum tubes: klystron, magnetron, traveling wave tube Solid state devices: FET, tunneling diodes, Gunn diodes 426A Heated cathode as electron source Tunable frequency from 9 to 10GHz; maximum output power 20mW Microwave oven magnetron; typical power kW 9

10 Russell Harrison Varian (April 24, 1898 July 28, 1959) Sigurd Fergus Varian (May 4, 1901 October 18, 1961) Varian Brothers...Klystron Tube (1940) 10

11 Generating of the microwaves. Klystron. Single transit klystron Reflection klystron Advantages: well defined frequencies, high power output High power klystron used in Canberra Deep Space Communications Complex (courtesy of Wikipedia) 11

12 Digital Volt Meter or Oscilloscope Digital Volt Meter or Oscilloscope attenuator horn horn Klystron frequency meter detector detector termination Microwave Transmitter Arm Microwave Receiver Arm 12

13 Experimental setup. Main components. Attenuator Klystron Frequency meter detector 13

14 Detector diode RF in RF choke Bypass capacitor V out I I 0 ev [exp 1] kt Typical I-V dependence for p-n diode Taylor expansion for exp function will give: exp( x) 1 And finally x If V=V 0 sint 2 x 2! 3 x 3!... b V2 0 2 I av 0(DC) 1 cos2ωt bv 2... I DC 2 V0 b

15 f c ~ 200GHz 15

16 Mirror A L R Mirror B Transmitter Beam splitter L R, L B optical paths (OP) for red and blue rays OP = n*l G n refraction index; L G geometrical length L B Receiver Albert Abraham Michelson ( ) The Nobel Prize in Physics 1907 Condition for constructive interference 2 L B R L n 16

17 Physics 403 Lab Michelson interferometer setup 17

18 r 1 r2 For constructive Interference Dr=n or dsinq=n Thomas Young ( ) Dr=r 1 -r 2 =dsinq b d q The measured envelope of the diffraction pattern can be defined as: 2 2 2sin x 2 0 ss cos ( kd sin( q / 2) x k where x kbsin( q / 2) 2 and is wave vector of the plane wave 18

19 Transmitter Physics 403 Lab setup and example of the data 19

20 2 2 2sin x 2 0 ss cos ( kd sin( q / 2) x x kbsin( q / 2) 200 =3.141cm Model Two_slit (User) Equation y=i0*(sin(k1*sin(pi*x/360+f))/(k1*sin(pi*x/360+f))) ^2 *(cos(k2*sin(pi*x/360+f)))^2+i00 Reduced Chi-Sqr I (na) 100 Adj. R-Square Value Standard Error I K K f E-04 I y = I q o Fitting equation sin(k1 sin πx 360 +f 2 K1 sin πx cos 2 K2 sin πx + f +I f 360 Here in fitting expression: I 0 = ψ 0 2 ; K1 = kb; K2 = kd 20

21 Mirror Transmitter h Receiver d1 Difference of the wave paths of red and blue rays is: d2 Humphry Lloyd DS h d1 h d 2 ( d1 d2) For constructive interference DS=n Lab setup picture 21

22 n 1 sinq 1 =n 2 sinq 2 Snell s law Willebrord Snellius q 1 n 1 >n 2 Claudius Ptolemaeus after AD 83 c.168) n 1 n 2 q 2 Equation for critical angle: n 1 sinq c =n 2 sin90 o q c =sin -1 (n 2 /n 1 ) 22

23 Transmitter n1(lucite) n2(air) Lucite prism 1.5 Experimental setup and the example of the data Signal intensity (A) Angle q 0 23

24 Transmitter Polarizer Transmitter Receiver Metallic grid q Etienne-Louis Malus Malus law E=E 0 cosq I E 2 I=I 0 cos 2 q 24

25 Transmitter Rotatable receiver Polarizer I=I 0 cos 2 q Experimental data 25

26 Interference of the EM waves reflected from the crystalline layers Sir William Henry Bragg William Lawrence Bragg The Nobel Prize in Physics 1915 "for their services in the analysis of crystal structure by means of X-rays" 26

27 (100) (110) (210) Different orientations of the crystal 27

28 n=2dsinq <2d In our experiment ~3cm; For cubic symmetry the angles of Bragg peaks can be calculated from: crystal 2 2 sin q 2d h k l where h,k,l are the Miller Indices. For crystal with d=5cm and =3cm the 3 first Bragg peaks for (100) orientation can be found at Experimental setup angles: ~17.5 o ; 36.9 o and 64.2 o 28

29 q q 29

30 4 Matthew Stupca Longxiang Zhang I (A) 2 (100) (110) (111) (200)(210) (211) (220) (300) (degree) *courtesy of Matthew Stupca 30

31 Bragg diffraction. X-rays nm X-ray tube *courtesy of Wikipedia 31

32 Bragg diffraction. X-rays. X-ray K-series spectral line wavelengths (nm) for some common target materials Target Kβ₁ Kβ₂ Kα₁ Kα₂ Fe Co Ni Cu Zr Mo David R. Lide, ed. (1994). CRC Handbook of Chemistry and Physics 75th edition. CRC Press. pp *courtesy of Matthew Stupca 32

33 Bragg diffraction. X-rays. *courtesy of Matthew Stupca 33

34 Comments and suggestions 1. Klystron is very hot and the high voltage (~300V) is applied to repeller. 2. You have to do 6 (!) experiment in one Lab session take care about time management. The most time consuming experiment is the Bragg diffraction. 3. Do not put on the tables any extra stuff this will cause extra reflections of microwaves and could result in smearing of the data. 4. This is two weeks experiment but the equipment for the week 2 will be different. Please finish all week 1 measurements until the end of this week Good luck! 34